(4u-5)(3+u)=0

Solution for (4u-5)(3+u)=0 equation:

Simplifying
(4u + -5)(3 + u) = 0

Reorder the terms:
(-5 + 4u)(3 + u) = 0

Multiply (-5 + 4u) * (3 + u)
(-5(3 + u) + 4u * (3 + u)) = 0
((3 * -5 + u * -5) + 4u * (3 + u)) = 0
((-15 + -5u) + 4u * (3 + u)) = 0
(-15 + -5u + (3 * 4u + u * 4u)) = 0
(-15 + -5u + (12u + 4u2)) = 0

Combine like terms: -5u + 12u = 7u
(-15 + 7u + 4u2) = 0

Solving
-15 + 7u + 4u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-3 + -1u)(5 + -4u) = 0

Subproblem 1
Set the factor '(-3 + -1u)' equal to zero and attempt to solve:

Simplifying
-3 + -1u = 0

Solving
-3 + -1u = 0

Move all terms containing u to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + -1u = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1u = 0 + 3
-1u = 0 + 3

Combine like terms: 0 + 3 = 3
-1u = 3

Divide each side by '-1'.
u = -3

Simplifying
u = -3
Subproblem 2
Set the factor '(5 + -4u)' equal to zero and attempt to solve:

Simplifying
5 + -4u = 0

Solving
5 + -4u = 0

Move all terms containing u to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -4u = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4u = 0 + -5
-4u = 0 + -5

Combine like terms: 0 + -5 = -5
-4u = -5

Divide each side by '-4'.
u = 1.25

Simplifying
u = 1.25
Solution
u = {-3, 1.25}